JSM 2013 Home
Online Program Home
My Program

Abstract Details

Activity Number: 548
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #310458
Title: Semiparametric Modeling of Nonautonomous Nonlinear Dynamical Systems with Application
Author(s): Siyuan Zhou*+ and Debashis Paul and Jie Peng
Companies: University of California, Davis and University of California, Davis and University of California, Davis
Keywords: nonautonomous dynamical systems ; nonlinear optimization ; Levenberg-Marquardt ; Berkeley Growth data
Abstract:

Continuous time dynamical systems arise in modeling various physical, chemical and biological systems. We propose a semi-parametric approach for modeling population-level data on systems governed by non-autonomous differential equations. This model includes an unknown common gradient function and multiplicative subject-specific effects on the rate of change of the states. These subject-specific effects are modeled as polynomials in time. We propose a procedure for fitting this model based on a hierarchical likelihood framework where the baseline gradient function g is represented in a B-spline basis. We also propose a computationally efficient model selection procedure based on approximate cross validation scores. We also introduce another model selection procedure based on the mean squared errors of empirical derivatives of observed and fitted trajectories. We show by simulation studies that the proposed estimation and model selection procedures work effectively for both sparse and dense measurements and at various noise levels. We apply the proposed method to the Berkeley Growth Data.


Authors who are presenting talks have a * after their name.

Back to the full JSM 2013 program




2013 JSM Online Program Home

For information, contact jsm@amstat.org or phone (888) 231-3473.

If you have questions about the Continuing Education program, please contact the Education Department.

The views expressed here are those of the individual authors and not necessarily those of the JSM sponsors, their officers, or their staff.

ASA Meetings Department  •  732 North Washington Street, Alexandria, VA 22314  •  (703) 684-1221  •  meetings@amstat.org
Copyright © American Statistical Association.